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Figure shows the standing waves pattern ...

Figure shows the standing waves pattern in a string at t = 0. Find out the equation of the standing wave where the amplitude of antinode is 2A.

Text Solution

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Let we assume the equation of standing waves is
`=A^'sin (omegat+phi)`
where `A^'=2A sin (kx+theta)`
`because x=0 "is node" rArr A^'=0,at x=0`
`2A sin theta=0 rArrtheta=0`
at t = 0 Particle at is at y = A and going towards mean position.
`rArr phi=(pi)/2+(pi)/3=(5pi)/6`
so eq. of standing waves is
`y=2A sin kx sin (omegat+(5pi)/6)`
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